On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (negative 1, negative 3) and (0, 0). Everything to the right of the line is shaded. The second dashed line has a negative slope and goes through (negative 2, 3) and (1, negative 3). Everything to the right of the line is shaded. A school is planning for an addition in some open space next to the current building. The existing building ends at the origin. The graph represents the system of equations that can be used to define the space for the addition. What is the system of equations that matches the graph? y ≤ 3x y > –2x – 1 y > 3x y ≤ –2x – 1 y < –3x y ≥ 2x – 1 y > –3x y ≤ 2x – 1

y ≤ 3x  and y > –2x – 1 (close answer)

Step-by-step explanation:

Line pass (-1 , -3) and (0 , 0)

slope = (0 - (-3)) / (0 - (-1)) = 3

y intercept = 0

y = 3x

Everything to the right of the line is shaded: (if include the line) y ≤ 3x

if not include the line and only everything to the right: y < 3x

Line pass (-2 , 3) and (1 , -3)

slope = (-3 - 3) / (1 - (-2)) = -2

y intercept = 3 - ((-2) x (-2)) = -1

y = -2x - 1

Everything to the right of the line is shaded: (if include the line) y ≥ -2x - 1

if not include the line and only everything to the right: y > -2x - 1

in all the options listed, only the first one y ≤ 3x  and y > –2x – 1 close to the equation above. But y ≤ 3x must include the line y=3x (noy mentioned in the question above)

And there is a very small triangle in the 3rd quadrant is in the territory of original building. It should be excluded from the addition.

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4